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Why is that? Both functions work identically

sage: E = (x^2 + 2*x + 1) / (x + 1)
sage: E
(x^2 + 2*x + 1)/(x + 1)
sage: E.full_simplify()
x + 1
sage: E.simplify_full()
x + 1

Actually one is an alias of the other

sage: E.full_simplify == E.simplify_full

I would rather update the documentation to mention that both names are valid.